The shooting happened at about 6.30pm when the 23-year-old victim was in a BMW car waiting at traffic lights in Burmantofts Street, near to the A64 flyover, which remains closed.
A silver Mazda 3 forced its way through the traffic and pulled alongside the BMW, before three men armed with bats or machetes began attacking the BMW.
one of the three produced what was believed to be a handgun and fired at the victim, who was sat in the front passenger seat. The men left the scene in the Mazda, reversing into a car behind it, causing damage, before making off down St Mary’s Street.
The large police cordon is currently in place in Burmantofts Street, near Beckett Street and Nippet Lane, while officers carry out searches and forensic examination.
And after speaking with a number of witnesses, the police are now appealing for anyone with information to come forward.
Detective Inspector Andy Farrell, of West Yorkshire Police Firearms Prevent Team, said: "We have already spoken to a number of witnesses but we would still like to hear from anyone who witnessed the incident or who has any information that could assist the investigation.
“We are particularly keen to hear from anyone who saw anyone acting suspiciously in Davies Avenue, Roundhay, where the silver Mazda 3 was abandoned and set on fire.
“We appreciate that incidents of this nature will cause understandable concern to the public but we are keen to reassure people that we have specialist officers who are working to identify those involved and take appropriate action. We are also liaising with our colleagues in the local neighbourhood policing team who will be increasing their presence in the area to reassure people.”
Anyone with any information is asked to contact the Firearms Prevent Team via 101 quoting Operation Flowwick or Crimestoppers, anonymously, on 0800 555 111.